Do pilots even have control over when the door closes? I thought that was a decision from the gate agent in coordination with operations. Sitting in F on my last flight I overheard the gate agent tell the crew that they were going to close the door 10 minutes early since everyone was onboard, but we would not push for 5-10 because they were still waiting on some bags. We pushed back a couple minutes after the scheduled departure (door close) time.
I also think the decision to pushback is dependant more on ATC and ground controllers than the pilots. No point in pushing back and running the engine/APU if you are in a ground hold. I can see closing the door in this case anyway since it frees the gate agent to close out the flight, pull back the jetway and move on to other gates/flights.